Definition

Describing a set of vectors that are both at right angles to each other and have a length of one.

Example

In mathematics, an orthonormal basis is essential for simplifying calculations in linear algebra.

Conversation

Hey, have you heard about orthonormal vectors in math class?

Yeah, I think they are really interesting!

I read that they need to be both orthogonal and normalized.

Exactly! It's cool how they preserve angles and lengths.

Synonyms & Antonyms

Root Explanation

Orthonormal → It is formed from "ortho-" (from Greek "orthos", meaning straight or correct) and "normal" (from Latin "normalis", meaning made according to a rule or standard). The word "orthonormal" refers to a set of vectors that are both orthogonal (perpendicular) and of unit length, adhering to the standard of being normalized.

Memory Tip

Think of 'straight' or 'correct' ('ortho-') and 'standard' ('normal') to remember that 'orthonormal' describes vectors that are both perpendicular and of unit length.

Visually Confused Words